Coupled analytical and finite element investigation of dynamic and cyclic response in cracked functionally graded beams

Abstract Offshore and marine structures increasingly utilise Functionally Graded Materials (FGMs) because of their superior stiffness and enhanced resistance to damage under combined vibration and cyclic loading induced by waves, wind and operational conditions. This study presents a combined analytical and finite element investigation into the dynamic behaviour of a cracked FGM cantilever beam compared with eight conventional offshore structural steels. A fracture-mechanics-based analytical model, incorporating crack-induced flexibility and stiffness degradation under cyclic loading within a continuum damage mechanics framework, was developed to predict the beam’s natural frequencies and validated against finite element results, with deviations below 2%. The postulated cracks were represented by predefined notches to simulate pre-existing structural damage or defects, with crack depth ratios of a/h = 0.233, 0.333, 0.4, & 0.5 introduced at different locations along the beam length. A nonlinear finite element model developed in ABAQUS was subsequently used to evaluate stress evolution, strain accumulation, and hysteretic force-displacement response under displacement-controlled cyclic loading. As the crack depth ratio increased, both the natural frequency and stiffness decreased, whereas stress concentration, strain accumulation, and hysteresis loop width increased, indicating greater energy dissipation and progressive stiffness degradation. Compared with conventional offshore steels, the FGM beam consistently exhibited higher natural frequencies, lower displacement amplitudes, and stable cyclic behaviour without significant strength degradation. The proposed analytical-numerical framework was further validated against published experimental results, confirming its reliability for assessing the coupled vibration and cyclic behaviour of cracked FGM beams for offshore structural applications.